Related papers: About Algorithm for Transformation of Logic Functi…

The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…

Understanding how information is dynamically accumulated and transformed in human reasoning has long challenged cognitive psychology, philosophy, and artificial intelligence. Existing accounts, from classical logic to probabilistic models,…

Logic gates can be written in terms of complex differential operators, where the inputs and outputs are holomorphic functions with several variables. Using the polar representation of complex numbers, we arrive at an immediate connection…

Latent reasoning offers a computation-efficient alternative to Chain-of-Thought but often suffers from performance degradation due to distributional misalignment and ambiguous chain definitions. Ideally, latent reasoning should function as…

The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…

Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…

While Large Language Models (LLMs) have demonstrated significant potential in natural language processing , complex general-purpose reasoning requiring multi-step logic, planning, and verification remains a critical bottleneck. Although…

We investigate the mechanisms underlying a range of list-processing tasks in LLMs, and we find that LLMs have learned to encode a compact, causal representation of a general filtering operation that mirrors the generic "filter" function of…

In this paper we propose that a restricted version of logical inference can be implemented with self-attention networks. We are aiming at showing that LLMs (Large Language Models) constructed with transformer networks can make logical…

Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…

The semantic foundations for logic programming are usually separated into two different approaches. The operational semantics, which uses SLD-resolution, the proof method that computes answers in logic programming, and the declarative…

These days, vast amounts of knowledge are available online, most of it in written form. Search engines help us access this knowledge, but aggregating, relating and reasoning with it is still a predominantly human effort. One of the key…

Multi-Task Learning (MTL) aims at boosting the overall performance of each individual task by leveraging useful information contained in multiple related tasks. It has shown great success in natural language processing (NLP). Currently, a…

In this paper, we propose a numerical method of Fourier transform based on hyperfunction theory. In the proposed method, we compute analytic functions called the defining functions, which give the desired Fourier transform as a…

Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds…

Synthesizing a program that realizes a logical specification is a classical problem in computer science. We examine a particular type of program synthesis, where the objective is to synthesize a strategy that reacts to a potentially…

The heterogeneity of tools that support temporal logic formulae poses several challenges in terms of interoperability. In particular, a standard syntax for temporal logic on finite traces, despite similar to the one for infinite traces, is…

We investigate the applicability of the formalism of quantum mechanics to everyday life. It seems to be directly relevant for situations in which the very act of coming to a conclusion or decision on one issue affects one's confidence about…

In this paper we examine the limitations of Large Language Models (LLMs) for complex reasoning tasks. Although recent works have started to employ formal languages as an intermediate representation for reasoning tasks, they often face…

There are two kinds of approaches for termination analysis of logic programs: "transformational" and "direct" ones. Direct approaches prove termination directly on the basis of the logic program. Transformational approaches transform a…